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** Burnside's lemma, a theorem of group theory

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Wikipedia

## Some Related Sentences

** and Burnside's

** and lemma

__**__Zorn's

__lemma__: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

__**__Tukey's

__lemma__: Every non-empty collection

**of**finite character has

**a**maximal element with respect to inclusion.

** and theorem

__**__Tarski's

__theorem__: For every infinite set A

**,**there is

**a**bijective map between the sets A and A × A.

__**__König's

__theorem__: Colloquially

**,**the sum

**of**

**a**sequence

**of**cardinals is strictly less than the product

**of**

**a**sequence

**of**larger cardinals.

__**__If S is

**a**set

**of**sentences

**of**first-order logic and B is

**a**consistent subset

**of**S

**,**then B is included in

**a**set that is maximal among consistent subsets

**of**S. The special case where S is the set

**of**all first-order sentences in

**a**given signature is weaker

**,**equivalent to the Boolean prime ideal

__theorem__; see the section " Weaker forms " below.

__**__The Vitali

__theorem__on the existence

**of**non-measurable sets which states that there is

**a**subset

**of**the real numbers that is not Lebesgue measurable.

__**__The Baire category

__theorem__about complete metric spaces

**,**and its consequences

**,**such as the open mapping

__theorem__and the closed graph

__theorem__.

__**__Gödel's completeness

__theorem__for first-order logic: every consistent set

**of**first-order sentences has

**a**completion.

__**__The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass

__theorem__); hence they are transcendental.

__**__More generally

**,**Rademacher's

__theorem__extends the differentiability result to Lipschitz mappings between Euclidean spaces:

**a**Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.

__**__Artin reciprocity law

**,**

**a**general

__theorem__in number

**theory**that provided

**a**partial solution to Hilbert's ninth problem

** and group

__**__In topology

**,**morphisms between topological spaces are called continuous maps

**,**and an automorphism

**of**

**a**topological space is

**a**homeomorphism

**of**the space to itself

**,**or self-homeomorphism ( see homeomorphism

__group__).

__**__Terminology

**of**the British Isles

**,**discusses the sometimes ambiguous or contentious names for parts

**of**the island

__group__

__**__Marching band

**,**

**a**

__group__

**of**performers that consist

**of**instrumental musicians who generally perform outdoors and incorporate some type

**of**marching ( and possibly other movements ) with their musical performance

__**__Social Security number with no dashes or spaces followed immediately by " USN ", space

**,**blood

__group__

__**__Fermentative hydrogen production

**,**the fermentative conversion

**of**organic substrate to biohydrogen manifested by

**a**diverse

__group__

**of**bacteria

__**__The Pferdestärke PS ( German translation

**of**horsepower ) is

**a**name for

**a**

__group__

**of**similar power measurements used in Germany around the end

**of**the 19th century

**,**all

**of**about one metric horsepower in size.

__**__Parabolic induction:

**a**method

**of**constructing

__group__representations

**of**

**a**reductive

__group__from representations

**of**its parabolic subgroups.

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